Transient heat-flow methods

For a more rapid method see hot-wire method for rapid, transient heat flow methods see thermal diffusivity. Thermal Ceding Test Refractories subject to repeated changes in temperature (thermal cycling) lose strength. ASTM... 

Transient-heat-flow Methods. The axial and radial heat-flow methods discussed above depend on attaining a steady-state condition within the test specimen. This boundary condition is readily understood theoretically and easy to test experimentally. A disadvantage lies in the long, sometimes mctremely long, times required to achieve the condition. Under certain circumstances thermal conductivity can he determined by transient methods, where test times are much shorter. However, boundary conditions are difficult to analyze theoretically and often very approximate models are used for calculational purposes. 

For other than flat plates, heat flux lines are seldom parallel, rarely steady. In transient heat flow, determination of the temperature at a given time and point within the load necessitates use of the finite element method. 

The heat flow in a system is transient, or unsteady, when the temperatures at various points in the system change with time. Since a change in temperature indicates a change in internal energy, we conclude that energy storage is associated with unsteady heat flow. Unsteady-heat-flow problems are more complex than are those of steady state and can often only be solved by approximate methods. 

Estimation of equivalent ullage and condensed masses for the case where the ullage volume is pressurized may be handled as indicated previously. When transfer occurs, the volume changes and the calculational method must allow for this effect. It is convenient to assume that the volume change is instantaneous at constant pressure. The operation is not adiabatic. Heat flow occurs which will raise the temperature of the newly emerged wall area from the liquid bulk temperature to the saturation temperature of the gas at the system pressure. After this transient effect, the gas to wall heat exchange is as dictated by (11) with the proper boundary conditions. These are discussed below. 

Richardson SM (1972) Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel. J Fluid Mech 56 609-618 Rizzo FJ, Shippy DJ (1970) A method of solution for certain problems of transient heat conduction. AIAA J 8 2004-2009... 

Transient 3D flow, ADI methods. Again, for purposes of illustration, consider the classical, dimensionless, 3D heat equation for u(x,y,t),... 

While we have demonstrated von Neumann s test for the transient heat equation, the stability test applies equally to iterative methods for elliptic equations describing steady flows. The (artificial) time levels t and t + At would refer to the approximate solutions obtained at consecutive iterations. The pressure solvers in Chapter 7 are examples of simple elliptic solvers that are stable in von Neumann s sense. Recall that the iterative method applied to single wells as it did to line fractures. Such a robust algorithm can be used to model general multilateral well drainhole trajectories where the overall topology can be arbitrarily defined by the driller or reservoir engineer. 

For a flat slab specimen of thickness h (m), the thermal conductivity X (W m K ) is the heat flux per unit of temperature gradient in the direction perpendicular to an isothermal surface and is a material constant defined by the one-dimensional Fourier equation X = Qh/A(Ti — Tq) where Q is the time rate of the heat flow (W), A the area (m ) on a selected isothermal surface, and T and T2 the temperatures of the hot and cold surfaces, respectively, and h the sample thickness (m). Several steady-state or transient methods are available to measure the thermal conductivity of organic and inorganic materials." The guarded-hotplate (ASTM F433), heat-flow (ASTM C518), and Colora ther-moconductometer methods are accurate for thick plastic samples with thermal conductivity of 0.1—10 W m K . In electronics, steady-state techniques... 

If a reaction is accompanied by a change in A//, then the temperature of that reaction sensed with time is a measure of the rate. Although the method has found little use generally, it can be linked to a stopped-flow apparatus and this allows the determination of the thermal properties of a transient. The heat of formation of an intermediate, which decomposes with k = 0.27 s , in the complicated luciferase-FMNH2 reaction with Oj can be measured by stopped-flow calorimetry. 

The TEOM is a promising tool for investigation of the influence of coke on adsorption and diffusion in catalysts. As a consequence of high flow rates of the carrier gas through the sample bed, the technique minimizes the external mass and heat transfer limitations in transient experiments without affecting the accuracy of the measurements. The data are not influenced by buoyancy and flow patterns, which are significant when conventional methods are used. 

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